A container is divided into two equal compartments by a partition. One compartme

Question

A container is divided into two equal compartments by a partition. One compartment is initially filled with helium at a temperature of 255 K; the other is filled with oxygen at a temperature of 311 K. Both gases are at the same pressure. If we remove the partition and allow the gases to mix, what will be their final temperature? (in K)

Explanation / Answer

First law of thermodynamics states that total heat added to the system is sum of work done by the system and change in internal energy.In this case, heat added is 0 and work done is also 0. Hence, change in internal energy is zero. energy final = energy initial =>(Cv(oxygen)+Cv(Helium))*Tf = Cv(oxygen)*T(oxy)+Cv(helium)*T(hel) heat capacity=Cv(oxygen) = R/(?-1) ˜ 0.661 kJ/(kg K) heat capacity=Cv(Helium) ˜ 5.193 kJ/(kg K) Tf = (0.661*311+5.193*255)/(0.661+5.193) = 261.3232 K

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